Shalom and thank you for your question!
Chibut hakever is a ‘punishment’ that purifies the body and the soul, from the residue of impurity resulting from physical enjoyment such as eating and drinking etc., because these activities affect the soul, which becomes more ‘gross’ or material through them. This causes a barrier between us and G-d in this world, and makes it more difficult for the soul when it ascends to the afterlife, to bask in the Divine Presence. For this reason the body must undergo Chibut haKever, which shakes it off, much as we would knock the dust off a rug in order to clean it. When the soul is thus cleansed, and it is free of love and desire for physicality, the soul is now free to be a vessel for the supernal spiritual delights awaiting it, and it is able to bask in radiance of the Divine Presence in the Garden of Eden.
The Talmud recounts the story of Rabbi Yehudah the Prince, (leader of his generation,) who lived in such opulence that “radishes were found on his table in all seasons,” which was apparently a sign of immense wealth. On his death-bed however, he raised his hands towards Heaven, and testified that he had not enjoyed for himself any of the benefits of his wealth at all. His lifestyle had been wealthy in order to increase the honor of the Torah. There are more stories of righteous leaders who lived in a grand manner, only for the sake of the honor of Torah scholars. However it has also been common that righteous people have shown an example of living modestly, showing that their highest priorities are learning Torah and keeping Mitzvot. The Rambam, (Maimonides) expresses the idea for most regular people, that one should not exaggerate either way, being too extravagant or too austere. The Sages teach us that all our deeds should be for the sake of Heaven. What this means in our daily life, is that we should try to remember and have in mind that we carry out our daily physical activities in order that we should have enough strength, and be rested enough, to learn Torah, do the Mitzvot, and try to hasten the Redemption. When this is our perspective, and we endeavor to focus on these goals, then our physical activities are not sins, but positive activities. Nevertheless, as stated above, because these activities are physical, there is a need to undergo a cleansing process due to the effect on our souls. The most beautiful furniture in a palace will still be somewhat the worse for wear and tear, and some chiseling may be necessary to refine it to its original splendor.
So how do we try to avoid the need for the cleansing process?
In the book ‘HaYom Yom’, compiled by the Lubavitcher Rebbe from the Previous Rebbe’s teachings, in the entry for the 7th of the Hebrew month, Tevet:
“To avert (the need for) Chibut haKever, one should recite words of Torah, Tehillim, etc. for one sixth of the 24 hours of the day.”
This is to say that one should spend as much time as possible saying Tehillim, repeating MIshnayot (the Lubavitcher Rebbe requested that people try to learn some Tehillim and Mishnayot by heart, so that they can recite them wherever they go, purifying the air,) in order to strengthen the existence of the world, in order to protect himself from Chibut haKever and Kaf haKela (another cleansing process,) and I order to merit great revelations.
The Rebbe also emphasized many times that when a person goes out of his way to help others, this refines him. Hopefully this also lessens the need for other refinement processes.
There are also sources that say that when a person goes to a gravesite to pray for the soul of the deceased, according to the formula of reciting the Tehillim which begin with the initials of the name of the deceased, (in Psalm 119, which has sets of pesukim beginning with each letter of the Hebrew alphabet,) or other prayers beginning with the letters of the deceased’s name, this is also helpful in redeeming one from Chibut haKever, as well as being beneficial for the soul of the deceased. In general all Torah and Mitzvot we do in this world benefit the souls of our departed relatives, and it is good to have this in mind.
Also, there are sources, and this is the custom in Chabad, that one should choose a pasuk from the Torah which begins with the first letter of one’s name and ends with the last letter of one’s name, and recite this pasuk towards the end of the Shemonah Esre prayer, before ‘Yehi Ratzon’. In this way we will not forget our names when the angel of death comes and asks us, for if we do we could incur severe judgements. Thus in Chabad we also say a pasuk with the Rebbe’s first and last letters as well, to remind the angel that we are connected to the Rebbe.
